Questions: For each of the regions listed in the following table, use the midpoint method to identify if the demand for this good is elastic, (approximately) unit elastic, or inelastic. Region Elastic Inelastic Unit Elastic ------------ Between W and X O ○ O Between Y and Z O 0 0 Between X and Y 0 0 O

For each of the regions listed in the following table, use the midpoint method to identify if the demand for this good is elastic, (approximately) unit elastic, or inelastic.

Region Elastic Inelastic Unit Elastic
------------
Between W and X O ○ O
Between Y and Z O 0 0
Between X and Y 0 0 O

Transcript text: For each of the regions listed in the following table, use the midpoint method to identify if the demand for this good is elastic, (approximately) unit elastic, or inelastic. \begin{tabular}{|c|c|c|c|} \hline Region & Elastic & Inelastic & Unit Elastic \\ \hline Between W and X & O & ○ & O \\ \hline Between $Y$ and $Z$ & O & 0 & 0 \\ \hline Between $X$ and $Y$ & 0 & 0 & O \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Identify the Points

Identify the coordinates of the points W, X, Y, and Z from the graph:

W: (70, 40)
X: (35, 140)
Y: (10, 280)
Z: (0, 280)

Step 2: Calculate the Midpoint Elasticity for W and X

Use the midpoint formula for elasticity between points W and X: \[ \text{Elasticity} = \frac{(Q_2 - Q_1)}{(Q_2 + Q_1)/2} \div \frac{(P_2 - P_1)}{(P_2 + P_1)/2} \] \[ Q_1 = 70, Q_2 = 35, P_1 = 40, P_2 = 140 \] \[ \text{Elasticity} = \frac{(35 - 70)}{(35 + 70)/2} \div \frac{(140 - 40)}{(140 + 40)/2} \] \[ \text{Elasticity} = \frac{-35}{52.5} \div \frac{100}{90} \] \[ \text{Elasticity} = -0.67 \div 1.11 \approx -0.60 \] Since the absolute value is less than 1, the demand is inelastic.

Step 3: Calculate the Midpoint Elasticity for Y and Z

Use the midpoint formula for elasticity between points Y and Z: \[ Q_1 = 10, Q_2 = 0, P_1 = 280, P_2 = 280 \] \[ \text{Elasticity} = \frac{(0 - 10)}{(0 + 10)/2} \div \frac{(280 - 280)}{(280 + 280)/2} \] Since the price does not change, the elasticity is undefined, but typically, if quantity changes with no price change, it is considered perfectly elastic.